Direct current electrical resistivity tomography (ERT) is a robust and well proven method of characterizing and monitoring the subsurface distribution of bulk electrical conductivity (Revil et al., 2012, Loke et al., 2013, Kemna et al., 2006). Electrical conductivity is a useful metric for understanding environmentally significant properties and processes because it is governed by pore fluid chemistry, porosity, pore connectivity, saturation, mineralogy, and grain size distribution (Slater and Lesmes, 2002, Revil and Glover, 1998, Lesmes and Friedman, 2005). In some cases, only one of these properties changes significantly in space or time, enabling spatial or temporal changes in ERT-derived bulk conductivity to characterize the property or process in a relatively unique manner.
ERT works by injecting current into the subsurface across a pair of electrodes, and measuring the corresponding electrical potential response across another pair of electrodes. Many such measurements are strategically taken across an array of electrodes to produce an ERT data set. These data are then processed through a computationally demanding process known as inversion to produce an image of the subsurface conductivity structure that gave rise to the measurements. Data can be inverted to provide 2D images, 3D images, or in the case of time-lapse 3D imaging, 4D images.
Spatial and/or temporal changes in conductivity caused by anthropogenic sources often originate from or are interspersed with buried metallic infrastructure (e.g. transfer pipes, well casings, and storage tanks). Being highly conductive, such infrastructure naturally tends to dominate and degrade ERT images, reducing or eliminating the utility of ERT imaging under otherwise favorable conditions. The forward model, a critical computational component of ERT imaging, is used to simulate ERT data. As discussed further herein, the forward model is the numerical solution to the Poisson equation, which provides the subsurface electrical potential arising from a known source of current and known conductivity distribution discretized within a numerical grid or mesh. Several authors have approached aspects of the infrastructure problem by modeling metallic well casings as a line of highly conductive cells relative to the background material (Zhu and Feng, 2011, Daily et al., 2004b, Daily et al., 2004a, Ramirez et al., 1996, Rucker, 2012, Rucker et al., 2012, Rucker et al., 2011, Rucker et al., 2010). Rucker et al., (2010) described the general approach, whereby vertically stacked rectangular cells of high conductivity are used to approximate a metallic well casing. To model the casing as a long current source electrode, a point source is placed within one of these cells, and the numerical solution is expected to adequately approximate current flow through the wellbore, and the corresponding constant potential that develops along the casing. The numerical inaccuracies with this approach for a large jump in conductivity at the wellbore interface are well documented (Hou and Liu, 2005, Kafafy et al., 2005, Liu et al., 2000, Yang, 2000). Namely, the conductive discontinuity at the wellbore causes the forward solution matrix to become ill-conditioned, with a condition number proportional to σmetal/σsoil, where σmetal and σsoil are respectively the conductivity of the well casing and the conductivity of the host material (Klapper and Shaw, 2007). For example, Rucker et al., (2010) noted inaccurate modeling results when modeling the wellbore at 10,000 S/m within a 0.01 S/m host material. To compensate, they used a wellbore conductivity of 167 S/m meter, noting that this provided the most accurate match to the analytic solution for a homogeneous halfspace. Actual conductivities for common metallic wellbore materials range from 1×106 to 7×106 S/m. Other infrastructure modeling applications to date include the work of Rücker and Günther (2011), who demonstrated an approach for accurately modeling non-point electrodes, but their method does not account for the influence of metallic objects which are not used as electrodes.
Forward models using the direct modeling approach described above on an orthogonal mesh suffer from another disadvantage in that arbitrary shapes of metallic structures are difficult to efficiently model, particularly considering the finely divided meshes necessary to model pipes and wells in true dimension. In addition, the direct modeling approach cannot accommodate situations where metallic structures are discontinuous in space, but electrically connected (e.g. buried tanks connected by above-ground piping, buried pipes with electrically insulated segments etc.). ERT is generally not well suited for environments with buried electrically conductive infrastructure such as pipes, tanks, or well casings, because these features tend to dominate and degrade ERT images. This reduces or eliminates the utility of ERT imaging where it would otherwise be highly useful for, for example, imaging fluid migration from leaking pipes, imaging soil contamination beneath leaking subsurface tanks, and monitoring contaminant migration in locations with dense networks of metal cased monitoring wells. Ignoring or inaccurately modeling metallic infrastructure is a significant source of forwarding modeling error. In practice, such errors compromise imaging results because the imaging algorithm compensates for forward modeling errors by incorrectly recovering the subsurface conductivity distribution.
The capability to produce ERT images with confidence in the presence of conductive infrastructure could be better assessed and significantly improved, through more accurate forward modeling. What is needed is a method of imaging the subsurface electrical conductivity distribution that removes the effects of the subsurface metallic structures.